JEE Main & Advanced Physics Magnetism Elements of Earth's Magnetic Field

The magnitude and direction of the magnetic field of the earth at a place are completely given by certain. quantities known as magnetic elements.

(1) Magnetic Declination \[(\theta )\]: It is the angle between geographic and the magnetic meridian planes.

Declination at a place is expressed at \[{{\theta }^{o}}E\] or \[{{\theta }^{o}}W\] depending upon whether the north pole of the compass needle lies to the east or to the west of the geographical axis.

(2) Angle of inclination or Dip \[(\phi )\] : It is the angle between the direction of intensity of total magnetic field of earth and a horizontal line in the magnetic meridian.

(3) Horizontal component of earth's magnetic field \[({{B}_{H}})\] : Earth's magnetic field is horizontal only at the magnetic equator. At any other place, the total intensity can be resolved into horizontal component \[({{B}_{H}})\] and vertical component \[({{B}_{V}})\].                

Also       \[{{B}_{H}}=B\cos \phi \]              ...... (i)  and        \[{{B}_{V}}=B\sin \varphi \]         ...... (ii)

By squaring and adding equation (i) and (ii)  \[B=\sqrt{{{B}_{{{H}^{2}}}}+{{B}_{{{V}^{2}}}}}\]

Dividing equation (ii) by equation (i)  \[\tan \varphi =\frac{{{B}_{V}}}{{{B}_{H}}}\]